The present invention relates to the temporal and spectral resolution of optical beams from free-electron lasers.
Free-electron laser (FEL) oscillators driven by pulsed RF linear accelerators (RF linacs) typically produce optical pulses of a duration determined by the width of the electron micropulses delivered by the linac. For example, the Mark III infrared FEL, which is driven by a 45 MeV, 2.856 GHz RF linac and delivers electron micropulses of several picoseconds duration, produces optical pulses with a characteristic width of .about. 2 ps and a separation of 350 ps (the RF period of the linac). In order for the optical pulses to build up from pass to pass within the oscillator, the cavity length must be close to the synchronous length, defined as that length for which the round trip time of a free-space optical pulse exactly matches a given integer multiple of the arrival time between adjacent electron micropulses; that integer also corresponds to the number of independently oscillating optical pulses contained within the cavity at any instant. These electron micropulses are grouped into macropulses with a 1-8 microsecond duration and a repetition rate on the order of several tens of Hertz. Therefore, each macropulse can yield many thousand outcoupled optical pulses, depending on its duration.
The fundamental limits to time resolution and spectral resolution in measurements using the optical beam of such an FEL are the width and spacing of the individual optical pulses generated by the FEL, and the degree of phase coherence between adjacent pulses in the pulse train. As indicated above, the optical pulse width is primarily determined by the duration of the electron micropulses, with further variations provided by the deviation of the cavity length from the synchronous length. The shortest optical pulses obtained to date have yielded a FWHM width of .about. 500 femtoseconds.
The spectral energy distribution is determined by the temporal variations of power and phase within the individual optical pulses, and by the absolute fluctuations of these quantities between and among the pulses in the pulse train. The temporal variations within the pulses yield a spectral envelope which can be no narrower than the transform limit defined by the inverse of the width of the optical pulses. This width would obtain if there were no temporal phase variations within the individual pulses, whereas the actual envelope may be broader if there are significant systematic or random phase variations within these pulses.
The modulation of the spectrum within this broad envelope is determined by the power and phase fluctuations between and among the individual pulses in the pulse train. In the Mark III FEL.sup.+, the individual optical pulses each complete a round trip through the cavity every 13.7 nanoseconds. Since all of the pulses within the cavity at any instant possess random relative phases (due to the random nature of the spontaneous radiation from which the pulses build up), that interval is also the smallest period at which the output pulses repeat themselves. The corresponding spectrum is a Fourier series consisting of a series of lines separated by 1/(13.7 ns) = 73 MHz filling the spectral envelope defined by the individual pulses. The width of these spectral lines is determined by the Q of the resonator and the noise introduced by spontaneous emission. Fractional widths .DELTA..lambda./.lambda. on the order of 10 .sup.-8 are attainable at the typical 5% outcouplings used in the Mark III (with &lt;2% extraneous cavity losses); the corresponding finesse of the resonator for these losses is .about.90. FNT +Benson, S. V., J. Schultz, B. A. Hooper, R. Crane, and J. M. J. Madey; "Status report on the Stanford Mark III infrared free-electron laser"; in Proceedings of the Ninth International Free-electron Laser Conference; P. Sprangle, C. M. Tang, J. Walsh, ed. (1987).